%------------------------------------------------------------------------------
% File     : ITP063_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : cardinal.ax [Gau19]
%          : HL4063_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  651 ( 284 unt; 135 typ;   0 def)
%            Number of atoms       : 1171 ( 447 equ)
%            Maximal formula atoms :   24 (   1 avg)
%            Number of connectives :  773 ( 118   ~;  21   |; 240   &)
%                                         ( 112 <=>; 282  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  105 (  64   >;  41   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  132 ( 132 usr;  19 con; 0-5 aty)
%            Number of variables   : 2284 (2094   !;  53   ?;2284   :)
%                                         ( 137  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: $tType > $tType ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: $tType ).

tff(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: $tType > $tType ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

tff(tyop_2Esum_2Esum,type,
    tyop_2Esum_2Esum: ( $tType * $tType ) > $tType ).

tff(app_2E2,type,
    app_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(p,type,
    p: tyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

tff(combin_k_2E0,type,
    combin_k_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(combin_s_2E0,type,
    combin_s_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Earithmetic_2E_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2A_2E2,type,
    c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Ecardinal_2E_2B__c_2E0,type,
    c_2Ecardinal_2E_2B__c_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2Ecardinal_2E_2B__c_2E2,type,
    c_2Ecardinal_2E_2B__c_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3E_3D_2E0,type,
    c_2Earithmetic_2E_3E_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3E_3D_2E2,type,
    c_2Earithmetic_2E_3E_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebool_2E_3F_21_2E0,type,
    c_2Ebool_2E_3F_21_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_3F_21_2E1,type,
    c_2Ebool_2E_3F_21_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2EBIGUNION_2E0,type,
    c_2Epred__set_2EBIGUNION_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EBIGUNION_2E1,type,
    c_2Epred__set_2EBIGUNION_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EBIJ_2E0,type,
    c_2Epred__set_2EBIJ_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EBIJ_2E3,type,
    c_2Epred__set_2EBIJ_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Epred__set_2ECARD_2E0,type,
    c_2Epred__set_2ECARD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).

tff(c_2Epred__set_2ECARD_2E1,type,
    c_2Epred__set_2ECARD_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ) ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).

tff(c_2Epred__set_2ECROSS_2E0,type,
    c_2Epred__set_2ECROSS_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2ECROSS_2E2,type,
    c_2Epred__set_2ECROSS_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EDELETE_2E0,type,
    c_2Epred__set_2EDELETE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EDELETE_2E2,type,
    c_2Epred__set_2EDELETE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EDIFF_2E0,type,
    c_2Epred__set_2EDIFF_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EDIFF_2E2,type,
    c_2Epred__set_2EDIFF_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EDISJOINT_2E0,type,
    c_2Epred__set_2EDISJOINT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EDISJOINT_2E2,type,
    c_2Epred__set_2EDISJOINT_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).

tff(c_2Earithmetic_2EEXP_2E0,type,
    c_2Earithmetic_2EEXP_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EEXP_2E2,type,
    c_2Earithmetic_2EEXP_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Epred__set_2EFINITE_2E0,type,
    c_2Epred__set_2EFINITE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Epred__set_2EFINITE_2E1,type,
    c_2Epred__set_2EFINITE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EGSPEC_2E1,type,
    c_2Epred__set_2EGSPEC_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ecardinal_2EHAS__SIZE_2E0,type,
    c_2Ecardinal_2EHAS__SIZE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Ecardinal_2EHAS__SIZE_2E2,type,
    c_2Ecardinal_2EHAS__SIZE_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2EIMAGE_2E0,type,
    c_2Epred__set_2EIMAGE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EIMAGE_2E2,type,
    c_2Epred__set_2EIMAGE_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2EINJ_2E0,type,
    c_2Epred__set_2EINJ_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EINJ_2E3,type,
    c_2Epred__set_2EINJ_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Esum_2EINL_2E0,type,
    c_2Esum_2EINL_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)) ).

tff(c_2Esum_2EINL_2E1,type,
    c_2Esum_2EINL_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Esum_2Esum(A_27a,A_27b) ) ).

tff(c_2Esum_2EINR_2E0,type,
    c_2Esum_2EINR_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)) ).

tff(c_2Esum_2EINR_2E1,type,
    c_2Esum_2EINR_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27b > tyop_2Esum_2Esum(A_27a,A_27b) ) ).

tff(c_2Epred__set_2EINSERT_2E0,type,
    c_2Epred__set_2EINSERT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EINSERT_2E2,type,
    c_2Epred__set_2EINSERT_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EINTER_2E0,type,
    c_2Epred__set_2EINTER_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EINTER_2E2,type,
    c_2Epred__set_2EINTER_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(c_2Ecombin_2EK_2E1,type,
    c_2Ecombin_2EK_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).

tff(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).

tff(c_2Elist_2ELENGTH_2E1,type,
    c_2Elist_2ELENGTH_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).

tff(c_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: 
      !>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: 
      !>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Epred__set_2EPOW_2E0,type,
    c_2Epred__set_2EPOW_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2EPOW_2E1,type,
    c_2Epred__set_2EPOW_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ) ).

tff(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).

tff(c_2Eoption_2ESOME_2E1,type,
    c_2Eoption_2ESOME_2E1: 
      !>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).

tff(c_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2ESUBSET_2E2,type,
    c_2Epred__set_2ESUBSET_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Enum_2ESUC_2E0,type,
    c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Enum_2ESUC_2E1,type,
    c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Epred__set_2ESURJ_2E0,type,
    c_2Epred__set_2ESURJ_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2ESURJ_2E3,type,
    c_2Epred__set_2ESURJ_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2Eoption_2ETHE_2E0,type,
    c_2Eoption_2ETHE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a) ).

tff(c_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).

tff(c_2Epair_2EUNCURRY_2E1,type,
    c_2Epair_2EUNCURRY_2E1: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).

tff(c_2Epred__set_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EUNION_2E2,type,
    c_2Epred__set_2EUNION_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Epred__set_2EUNIV_2E0,type,
    c_2Epred__set_2EUNIV_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Ecardinal_2Ebijns_2E0,type,
    c_2Ecardinal_2Ebijns_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)) ).

tff(c_2Ecardinal_2Ebijns_2E1,type,
    c_2Ecardinal_2Ebijns_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool) ) ).

tff(c_2Ecardinal_2Ecardeq_2E0,type,
    c_2Ecardinal_2Ecardeq_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ecardinal_2Ecardeq_2E2,type,
    c_2Ecardinal_2Ecardeq_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ecardinal_2Ecardgeq_2E0,type,
    c_2Ecardinal_2Ecardgeq_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ecardinal_2Ecardgeq_2E2,type,
    c_2Ecardinal_2Ecardgeq_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ecardinal_2Ecardgt_2E0,type,
    c_2Ecardinal_2Ecardgt_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ecardinal_2Ecardgt_2E2,type,
    c_2Ecardinal_2Ecardgt_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Ecardinal_2Ecardleq_2E0,type,
    c_2Ecardinal_2Ecardleq_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ecardinal_2Ecardleq_2E2,type,
    c_2Ecardinal_2Ecardleq_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(c_2Epred__set_2Ecount_2E0,type,
    c_2Epred__set_2Ecount_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Epred__set_2Ecount_2E1,type,
    c_2Epred__set_2Ecount_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2Epred__set_2Ecountable_2E0,type,
    c_2Epred__set_2Ecountable_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Epred__set_2Ecountable_2E1,type,
    c_2Epred__set_2Ecountable_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Ecardinal_2Elist_2E0,type,
    c_2Ecardinal_2Elist_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)) ).

tff(c_2Ecardinal_2Elist_2E1,type,
    c_2Ecardinal_2Elist_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ) ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Ecombin_2Eo_2E2,type,
    c_2Ecombin_2Eo_2E2: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

tff(c_2Ecardinal_2Eset__exp_2E0,type,
    c_2Ecardinal_2Eset__exp_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))) ).

tff(c_2Ecardinal_2Eset__exp_2E2,type,
    c_2Ecardinal_2Eset__exp_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool) ) ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
     => ( V0f_2E0 = V1g_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Eboolext,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Etruth,axiom,
    p(c_2Ebool_2ET_2E0) ).

tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
    ~ p(c_2Ebool_2EF_2E0) ).

tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Es__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).

tff(logicdef_2E_2F_5C,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(logicdef_2E_5C_2F,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(logicdef_2E_7E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(logicdef_2E_3D_3D_3E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
      ( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
    <=> ( V0_2E0 = V1_2E0 ) ) ).

tff(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
    <=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
    <=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27c),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(A_27a,tyop_2Esum_2Esum(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2E_2B__c_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool)),c_2Ecardinal_2E_2B__c_2E0(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a,X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Epair_2E_2C_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27a,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27b,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(A_27c,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(A_27c,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(A_27a,A_27b),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
      ( ( X0_2E0 = X1_2E0 )
    <=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3E_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3E_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_21_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_21_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EBIGUNION_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIGUNION_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Epred__set_2EBIGUNION_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),X0_2E0) ) ).

tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(A_27a,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(A_27a,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EBIJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27b),X2_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27c_29,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27c),X2_2E0: tyop_2Eoption_2Eoption(A_27c)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27c),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27c),app_2E2(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27c)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27c),tyop_2Eoption_2Eoption(A_27c))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27c)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27c),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27a,tyop_2Esum_2Esum(A_27b,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Emin_2Ebool,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Emin_2Ebool,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool)),c_2Epred__set_2ECROSS_2E0(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: A_27a] : ( c_2Epred__set_2EDELETE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDIFF_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDISJOINT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDISJOINT_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDISJOINT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDISJOINT_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EEXP_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEXP_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EEXP_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Esum_2Esum(A_27a,A_27b),A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Esum_2Esum(A_27a,A_27b),A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27b,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Esum_2Esum(A_27a,A_27b),A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Esum_2Esum(A_27a,A_27b),A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))] : ( c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2EHAS__SIZE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecardinal_2EHAS__SIZE_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2EHAS__SIZE_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ecardinal_2EHAS__SIZE_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecardinal_2EHAS__SIZE_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2EHAS__SIZE_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecardinal_2EHAS__SIZE_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2EHAS__SIZE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecardinal_2EHAS__SIZE_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esum_2Esum(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINJ_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EINJ_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27a] : ( c_2Esum_2EINL_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b] : ( c_2Esum_2EINR_2E1(A_27a,A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Ecombin_2EK_2E1(tyop_2Eoption_2Eoption(A_27b),A_27a,X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2EK_2E0(tyop_2Eoption_2Eoption(A_27b),A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EPOW_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EPOW_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EPOW_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Eoption_2ESOME_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: A_27c] : ( c_2Eoption_2ESOME_2E1(A_27c,X0_2E0) = app_2E2(A_27c,tyop_2Eoption_2Eoption(A_27c),c_2Eoption_2ESOME_2E0(A_27c),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Epred__set_2ESURJ_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESURJ_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESURJ_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))] : ( c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E0(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ecardinal_2Ebijns_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ebijns_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Ecardinal_2Ebijns_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecardinal_2Ebijns_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ebijns_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),c_2Ecardinal_2Ebijns_2E0(A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a,tyop_2Esum_2Esum(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27a1_20mono_2EA_27a2,axiom,
    ! [A_27a1: $tType,A_27a2: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a1,A_27a2,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27a1,A_27a2),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27b1_20mono_2EA_27b2,axiom,
    ! [A_27b1: $tType,A_27b2: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27b1,A_27b2,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27b1,A_27b2),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27b_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b1_2Ctyop_2Eoption_2Eoption_28A_27a1_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b2_2Ctyop_2Eoption_2Eoption_28A_27a2_29_29,axiom,
    ! [A_27a1: $tType,A_27a2: $tType,A_27b1: $tType,A_27b2: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27d_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Esum_2Esum_28A_27b_2CA_27c_29_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Epair_2Eprod_28A_27a_2CA_27c_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2CA_27c_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Epair_2Eprod_28A_27a_2CA_27c_29_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27c_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Esum_2Esum(A_27a,A_27b),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27b,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27b,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27c_29_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27d_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardeq_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2Ctyop_2Esum_2Esum_28A_27b_2CA_27c_29_29_20mono_2Etyop_2Esum_2Esum_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Esum_2Esum(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardeq_2E0(tyop_2Esum_2Esum(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Esum_2Esum(tyop_2Esum_2Esum(A_27a,A_27b),A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardgeq_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardgeq_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardgeq_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardgeq_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardgeq_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardgeq_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardgt_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardgt_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardgt_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,tyop_2Esum_2Esum(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27a,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27b,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27b,tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27b,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27c_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27c,tyop_2Esum_2Esum(A_27a,A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27c,tyop_2Esum_2Esum(A_27a,A_27b)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27d_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27d,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27d,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2EA_27d_20mono_2EA_27c,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(A_27d,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(A_27d,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27a_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27d_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Esum_2Esum(A_27a,A_27b),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27c_29_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27d_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Ecardleq_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27b_2CA_27d_29_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27c_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27a,A_27c),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ecardinal_2Ecardleq_2E0(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27a,A_27c)),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecount_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(A_27b),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(A_27c),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2Ecountable_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2Ecountable_2E0(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecardinal_2Elist_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Elist_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Ecardinal_2Elist_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27a,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,A_27a)),c_2Ecombin_2Eo_2E0(A_27a,A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27b1_20mono_2EA_27a1,axiom,
    ! [A_27a1: $tType,A_27b1: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27b1,A_27a1,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27b1,A_27a1),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27b2_20mono_2EA_27a2,axiom,
    ! [A_27a2: $tType,A_27b2: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27b2,A_27a2,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27b2,A_27a2),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27d_20mono_2EA_27c,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27d,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27d,A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(tyop_2Epair_2Eprod(A_27b,A_27a),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: $tType,A_27d: $tType,X0_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27c,A_27d,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27c,A_27d),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ecardinal_2Eset__exp_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),tyop_2Emin_2Ebool)),c_2Ecardinal_2Eset__exp_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardleq__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0))
    <=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2EINJ_2E3(A_27a,A_27b,V2f_2E0,V0s1_2E0,V1s2_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardeq__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0))
    <=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V2f_2E0,V0s1_2E0,V1s2_2E0)) ) ).

tff(thm_2Ecardinal_2EHAS__SIZE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V1n_2E0))
    <=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = V1n_2E0 ) ) ) ).

tff(thm_2Ecardinal_2Elist__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)))] :
      ( ! [V1l_2E0: tyop_2Elist_2Elist(A_27a),V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1l_2E0),V0A_2E0))
        <=> ! [V2e_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1l_2E0)))
             => p(c_2Ebool_2EIN_2E2(A_27a,V2e_2E0,V0A_2E0)) ) )
     => ( ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1l_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V1l_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1l_2E0),V0A_2E0)) )
       => ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Elist_2E1(A_27a,V0A_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2Ebijns__def,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)))] :
      ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1f_2E0),V0A_2E0))
        <=> ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27a,c_2Ecombin_2Eo_2E2(A_27a,A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ETHE_2E0(A_27a),V1f_2E0),V0A_2E0,V0A_2E0))
            & ! [V2a_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V0A_2E0))
              <=> ? [V3b_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),V1f_2E0,V2a_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3b_2E0) ) ) ) )
     => ( ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1f_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool,V1f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1f_2E0),V0A_2E0)) )
       => ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ebijns_2E1(A_27a,V0A_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2Ecardgeq__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardgeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0) ) ).

tff(thm_2Ecardinal_2Ecardgt__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardgt_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
    <=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2Eadd__c,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)))] :
      ( ! [V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),F1_2E0,V1t_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Esum_2EINR_2E1(A_27a,A_27b,V3y_2E0),c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1t_2E0)) )
     => ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0,V0s_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Esum_2EINL_2E1(A_27a,A_27b,V2x_2E0),c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0)) )
       => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Epred__set_2EUNION_2E2(tyop_2Esum_2Esum(A_27a,A_27b),c_2Epred__set_2EGSPEC_2E1(tyop_2Esum_2Esum(A_27a,A_27b),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),F0_2E0,V0s_2E0)),c_2Epred__set_2EGSPEC_2E1(tyop_2Esum_2Esum(A_27a,A_27b),A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Emin_2Ebool)),F1_2E0,V1t_2E0))) ) ) ) ).

tff(thm_2Ecardinal_2Eset__exp__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))))] :
      ( ! [V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F1_2E0,V1B_2E0),V0A_2E0),V2f_2E0))
        <=> ( ! [V3b_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V3b_2E0,V1B_2E0))
               => ? [V4a_2E0: A_27b] :
                    ( p(c_2Ebool_2EIN_2E2(A_27b,V4a_2E0,V0A_2E0))
                    & ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),V2f_2E0,V3b_2E0) = c_2Eoption_2ESOME_2E1(A_27b,V4a_2E0) ) ) )
            & ! [V5b_2E0: A_27a] :
                ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V5b_2E0,V1B_2E0))
               => ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),V2f_2E0,V5b_2E0) = c_2Eoption_2ENONE_2E0(A_27b) ) ) ) )
     => ( ! [V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))),F0_2E0,V1B_2E0),V0A_2E0),V2f_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool,V2f_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),F1_2E0,V1B_2E0),V0A_2E0),V2f_2E0)) )
       => ! [V0A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V0A_2E0,V1B_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool))),F0_2E0,V1B_2E0),V0A_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__MUL__LT__LEMMA,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V2u_2E0,V1t_2E0))
        & ~ p(c_2Epred__set_2EFINITE_2E1(A_27c,V2u_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b),V2u_2E0,c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__LT__ADD,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1s_27_2E0,V0s_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27d,A_27c,V3t_27_2E0,V2t_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27b,A_27d),tyop_2Esum_2Esum(A_27a,A_27c),c_2Ecardinal_2E_2B__c_2E2(A_27b,A_27d,V1s_27_2E0,V3t_27_2E0),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27c,V0s_2E0,V2t_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__ADD2__ABSORB__LT,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27c,V2u_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V2u_2E0,V1t_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,tyop_2Esum_2Esum(A_27a,A_27b),V2u_2E0,c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__ADD__ABSORB,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27b,c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__MUL__ABSORB,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__ADD2__ABSORB__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27c,V2u_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27c,c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),V2u_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__ADD__ABSORB__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27b,c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__MUL2__ABSORB__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27c,V2u_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),V2u_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__MUL__ABSORB__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b,c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__BIGUNION,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V1k_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1k_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,V0s1_2E0,V1k_2E0))
        & ! [V2e_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2e_2E0,V0s1_2E0))
           => p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V2e_2E0,V1k_2E0)) ) )
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27b,V0s1_2E0),V1k_2E0)) ) ).

tff(thm_2Ecardinal_2ESET__SUM__CARDEQ__SET,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Ebool,A_27a),V0s_2E0,c_2Epred__set_2ECROSS_2E2(tyop_2Emin_2Ebool,A_27a,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Ebool))),V0s_2E0)))
        & ! [V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2B_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( ( p(c_2Epred__set_2EDISJOINT_2E2(A_27b,V1A_2E0,V2B_2E0))
              & p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,V1A_2E0,V0s_2E0))
              & p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,V2B_2E0,V0s_2E0)) )
           => p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,c_2Epred__set_2EUNION_2E2(A_27b,V1A_2E0,V2B_2E0),V0s_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2ESET__SQUARED__CARDEQ__SET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0),V0s_2E0)) ) ).

tff(thm_2Ecardinal_2Eset__binomial2,axiom,
    ! [A_27a: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1A_2E0,V0B_2E0),c_2Epred__set_2EUNION_2E2(A_27a,V1A_2E0,V0B_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epred__set_2EUNION_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V1A_2E0,V1A_2E0),c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V1A_2E0,V0B_2E0)),c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V0B_2E0,V1A_2E0)),c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V0B_2E0,V0B_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardleq__empty,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
    <=> ( V0x_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).

tff(thm_2Ecardinal_2Ecardleq__lt__trans,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V2u_2E0,V1t_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardlt__leq__trans,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardlt__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V1t_2E0,V0s_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V2u_2E0,V1t_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V2u_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardlt__lenoteq,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
    <=> ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & ~ p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ) ).

tff(thm_2Ecardinal_2Ecardlt__REFL,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ~ ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).

tff(thm_2Ecardinal_2Ecardleq__lteq,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0))
    <=> ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1s2_2E0,V0s1_2E0))
        | p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0)) ) ) ).

tff(thm_2Ecardinal_2Ecardleq__dichotomy,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
      | p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2Ecountable__cardeq,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
     => ( c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0) = c_2Epred__set_2Ecountable_2E1(A_27b,V1t_2E0) ) ) ).

tff(thm_2Ecardinal_2Ecountable__thm,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Enum_2Enum,V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)) ) ).

tff(thm_2Ecardinal_2EIMAGE__cardleq__rwt,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1s_2E0,V2t_2E0))
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27c,V0f_2E0,V1s_2E0),V2t_2E0)) ) ).

tff(thm_2Ecardinal_2ESUBSET__CARDLEQ,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0x_2E0,V1y_2E0))
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0x_2E0,V1y_2E0)) ) ).

tff(thm_2Ecardinal_2ECARDLEQ__CROSS__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1s_27_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27d,V2t_2E0,V3t_27_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,V0s_2E0,V2t_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27d,V1s_27_2E0,V3t_27_2E0))) ) ).

tff(thm_2Ecardinal_2EIMAGE__cardleq,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),V1s_2E0)) ).

tff(thm_2Ecardinal_2EINFINITE__UNIV__INF,axiom,
    ! [A_27a: $tType] : ~ p(c_2Epred__set_2EFINITE_2E1(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a),c_2Epred__set_2EUNIV_2E0(tyop_2Esum_2Esum(tyop_2Enum_2Enum,A_27a)))) ).

tff(thm_2Ecardinal_2ECARDLEQ__FINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARDEQ__CARDLEQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0t2_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V1t1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V3s1_2E0,V2s2_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,V1t1_2E0,V0t2_2E0)) )
     => ( c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V3s1_2E0,V1t1_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27d,V2s2_2E0,V0t2_2E0) ) ) ).

tff(thm_2Ecardinal_2ECARDEQ__SUBSET__CARDLEQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0))
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARDEQ__CROSS__SYM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27a,V0t_2E0,V1s_2E0))) ).

tff(thm_2Ecardinal_2ECARDEQ__CROSS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0t2_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V1t1_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V2s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V3s1_2E0,V2s2_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,V1t1_2E0,V0t2_2E0)) )
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,V3s1_2E0,V1t1_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27d,V2s2_2E0,V0t2_2E0))) ) ).

tff(thm_2Ecardinal_2EFINITE__CLE__INFINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
        & ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V0t_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0)) ) ).

tff(thm_2Ecardinal_2EEMPTY__CARDLEQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,c_2Epred__set_2EEMPTY_2E0(A_27a),V0t_2E0)) ).

tff(thm_2Ecardinal_2ECARDEQ__INSERT__RWT,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
     => p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0),V1s_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardeq__INSERT,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0),V1s_2E0))
    <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,V1s_2E0))
        | ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARDEQ__0,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
      <=> ( V0x_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
      & ( p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27a,c_2Epred__set_2EEMPTY_2E0(A_27c),V0x_2E0))
      <=> ( V0x_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).

tff(thm_2Ecardinal_2ECARDEQ__CARD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0)) )
     => ( c_2Epred__set_2ECARD_2E1(A_27a,V1s1_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V0s2_2E0) ) ) ).

tff(thm_2Ecardinal_2ECARDEQ__FINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0))
     => ( c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0) = c_2Epred__set_2EFINITE_2E1(A_27b,V0s2_2E0) ) ) ).

tff(thm_2Ecardinal_2Ecardleq__ANTISYM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) )
     => p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardleq__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardleq__REFL,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).

tff(thm_2Ecardinal_2Ecardeq__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
     => p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardeq__SYM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0) ) ).

tff(thm_2Ecardinal_2Ecardeq__REFL,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).

tff(thm_2Ecardinal_2ESURJECTIVE__ON__RIGHT__INVERSE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ! [V3y_2E0: A_27b] :
          ( p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V2t_2E0))
         => ? [V4x_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
              & ( app_2E2(A_27a,A_27b,V1f_2E0,V4x_2E0) = V3y_2E0 ) ) )
    <=> ? [V5g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
        ! [V6y_2E0: A_27b] :
          ( p(c_2Ebool_2EIN_2E2(A_27b,V6y_2E0,V2t_2E0))
         => ( p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(A_27b,A_27a,V5g_2E0,V6y_2E0),V0s_2E0))
            & ( app_2E2(A_27a,A_27b,V1f_2E0,app_2E2(A_27b,A_27a,V5g_2E0,V6y_2E0)) = V6y_2E0 ) ) ) ) ).

tff(thm_2Ecardinal_2ESURJECTIVE__RIGHT__INVERSE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
      ( ! [V1y_2E0: A_27a] :
        ? [V2x_2E0: A_27b] : ( app_2E2(A_27b,A_27a,V0f_2E0,V2x_2E0) = V1y_2E0 )
    <=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
        ! [V4y_2E0: A_27a] : ( app_2E2(A_27b,A_27a,V0f_2E0,app_2E2(A_27a,A_27b,V3g_2E0,V4y_2E0)) = V4y_2E0 ) ) ).

tff(thm_2Ecardinal_2EFINITE__IMAGE__INJ__GENERAL,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
      ( ! [V5x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V5x_2E0),V2s_2E0),V0f_2E0),V1A_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V2s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0),V1A_2E0)) ) )
     => ( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2s_2E0),V0f_2E0),V1A_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V5x_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V5x_2E0),V2s_2E0),V0f_2E0),V1A_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
                  ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
                    & p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V2s_2E0))
                    & ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) ) )
                 => ( V3x_2E0 = V4y_2E0 ) )
              & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1A_2E0)) )
           => p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2s_2E0),V0f_2E0),V1A_2E0)))) ) ) ) ).

tff(thm_2Ecardinal_2EFINITE__IMAGE__INJ,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1A_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0),V1A_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
                ( ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) )
               => ( V2x_2E0 = V3y_2E0 ) )
            & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1A_2E0)) )
         => p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1A_2E0)))) ) ) ).

tff(thm_2Ecardinal_2EFINITE__IMAGE__INJ__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
            & ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
         => ( V2x_2E0 = V3y_2E0 ) )
     => ( c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)) = c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0) ) ) ).

tff(thm_2Ecardinal_2EINFINITE__IMAGE__INJ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
          ( ( app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V2y_2E0) )
         => ( V1x_2E0 = V2y_2E0 ) )
     => ! [V3s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V3s_2E0))
         => ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V3s_2E0))) ) ) ).

tff(thm_2Ecardinal_2EINFINITE__NONEMPTY,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).

tff(thm_2Ecardinal_2EFINITE__PRODUCT__DEPENDENT,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))))] :
      ( ! [V4x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5y_2E0: A_27b,V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),F1_2E0,V4x_2E0),V1s_2E0),V5y_2E0),V2t_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27b,V5y_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0,V4x_2E0))) ) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4x_2E0: A_27a,V5y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))),F0_2E0,V0f_2E0),V1s_2E0),V2t_2E0),V4x_2E0),V5y_2E0) = c_2Epair_2E_2C_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V4x_2E0),V5y_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),F1_2E0,V4x_2E0),V1s_2E0),V5y_2E0),V2t_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
              & ! [V3x_2E0: A_27a] :
                  ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
                 => p(c_2Epred__set_2EFINITE_2E1(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0,V3x_2E0))) ) )
           => p(c_2Epred__set_2EFINITE_2E1(A_27c,c_2Epred__set_2EGSPEC_2E1(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))),F0_2E0,V0f_2E0),V1s_2E0),V2t_2E0))))) ) ) ) ).

tff(thm_2Ecardinal_2EFINITE__PRODUCT,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))))] :
      ( ! [V2x_2E0: A_27a,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3y_2E0: A_27b,V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0s_2E0),V3y_2E0),V1t_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1t_2E0)) ) )
     => ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0s_2E0),V1t_2E0),V2x_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0s_2E0),V3y_2E0),V1t_2E0)) )
       => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
              & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) )
           => p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0s_2E0),V1t_2E0))))) ) ) ) ).

tff(thm_2Ecardinal_2ESURJECTIVE__IMAGE__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)))] :
      ( ! [V3P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V3P_2E0),V0f_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,app_2E2(A_27b,tyop_2Emin_2Ebool,V3P_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0))) )
     => ( ! [V3P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5x_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V3P_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,V5x_2E0,app_2E2(A_27b,tyop_2Emin_2Ebool,V3P_2E0,V5x_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
            ( ! [V1y_2E0: A_27b] :
              ? [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = V1y_2E0 )
          <=> ! [V3P_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V3P_2E0),V0f_2E0))) = c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V3P_2E0)) ) ) ) ) ).

tff(thm_2Ecardinal_2ESURJECTIVE__ON__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2v_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ! [V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2Epred__set_2ESUBSET_2E2(A_27b,V3t_2E0,V2v_2E0))
         => ? [V4s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V4s_2E0,V1u_2E0))
              & ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V4s_2E0) = V3t_2E0 ) ) )
    <=> ! [V5y_2E0: A_27b] :
          ( p(c_2Ebool_2EIN_2E2(A_27b,V5y_2E0,V2v_2E0))
         => ? [V6x_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V1u_2E0))
              & ( app_2E2(A_27a,A_27b,V0f_2E0,V6x_2E0) = V5y_2E0 ) ) ) ) ).

tff(thm_2Ecardinal_2ESURJECTIVE__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
        ? [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2s_2E0) = V1t_2E0 )
    <=> ! [V3y_2E0: A_27b] :
        ? [V4x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = V3y_2E0 ) ) ).

tff(thm_2Ecardinal_2ECARD__LE__INJ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0))) )
     => ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
          ( p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V0s_2E0),V1t_2E0))
          & ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
              ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
                & p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V0s_2E0))
                & ( app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V4y_2E0) ) )
             => ( V3x_2E0 = V4y_2E0 ) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__IMAGE__INJ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
              & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
              & ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
           => ( V2x_2E0 = V3y_2E0 ) )
        & p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0)) )
     => ( c_2Epred__set_2ECARD_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)) = c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0) ) ) ).

tff(thm_2Ecardinal_2ECARD__IMAGE__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
     => p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)),c_2Epred__set_2ECARD_2E1(A_27a,V1s_2E0))) ) ).

tff(thm_2Ecardinal_2ESURJECTIVE__IFF__INJECTIVE__GEN,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0) )
        & p(c_2Epred__set_2ESUBSET_2E2(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V2f_2E0,V0s_2E0),V1t_2E0)) )
     => ( ! [V3y_2E0: A_27b] :
            ( p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1t_2E0))
           => ? [V4x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
                & ( app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0) = V3y_2E0 ) ) )
      <=> ! [V5x_2E0: A_27a,V6y_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0))
              & p(c_2Ebool_2EIN_2E2(A_27a,V6y_2E0,V0s_2E0))
              & ( app_2E2(A_27a,A_27b,V2f_2E0,V5x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V6y_2E0) ) )
           => ( V5x_2E0 = V6y_2E0 ) ) ) ) ).

tff(thm_2Ecardinal_2ESURJECTIVE__IFF__INJECTIVE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27a)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27a,V1f_2E0,V0s_2E0),V0s_2E0)) )
     => ( ! [V2y_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V2y_2E0,V0s_2E0))
           => ? [V3x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
                & ( app_2E2(A_27a,A_27a,V1f_2E0,V3x_2E0) = V2y_2E0 ) ) )
      <=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
            ( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
              & p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V0s_2E0))
              & ( app_2E2(A_27a,A_27a,V1f_2E0,V4x_2E0) = app_2E2(A_27a,A_27a,V1f_2E0,V5y_2E0) ) )
           => ( V4x_2E0 = V5y_2E0 ) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__BIJECTION,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0) ) )
     => ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
          ( ! [V3x_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
             => p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0),V1t_2E0)) )
          & ! [V4y_2E0: A_27b] :
              ( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V1t_2E0))
             => ? [V5x_2E0: A_27a] :
                  ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0))
                  & ( app_2E2(A_27a,A_27b,V2f_2E0,V5x_2E0) = V4y_2E0 ) ) )
          & ! [V6x_2E0: A_27a,V7y_2E0: A_27a] :
              ( ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V0s_2E0))
                & p(c_2Ebool_2EIN_2E2(A_27a,V7y_2E0,V0s_2E0))
                & ( app_2E2(A_27a,A_27b,V2f_2E0,V6x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V7y_2E0) ) )
             => ( V6x_2E0 = V7y_2E0 ) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__BIJECTIONS,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0) ) )
     => ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
          ( ! [V4x_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
             => ( p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0),V1t_2E0))
                & ( app_2E2(A_27b,A_27a,V3g_2E0,app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0)) = V4x_2E0 ) ) )
          & ! [V5y_2E0: A_27b] :
              ( p(c_2Ebool_2EIN_2E2(A_27b,V5y_2E0,V1t_2E0))
             => ( p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(A_27b,A_27a,V3g_2E0,V5y_2E0),V0s_2E0))
                & ( app_2E2(A_27a,A_27b,V2f_2E0,app_2E2(A_27b,A_27a,V3g_2E0,V5y_2E0)) = V5y_2E0 ) ) ) ) ) ).

tff(thm_2Ecardinal_2ESING__SUBSET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0: A_27a] : ( c_2Epred__set_2ESUBSET_2E2(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V1x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),V0s_2E0) = c_2Ebool_2EIN_2E2(A_27a,V1x_2E0,V0s_2E0) ) ).

tff(thm_2Ecardinal_2EINJECTIVE__ON__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1u_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V2s_2E0,V1u_2E0))
            & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V3t_2E0,V1u_2E0))
            & ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2s_2E0) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V3t_2E0) ) )
         => ( V2s_2E0 = V3t_2E0 ) )
    <=> ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1u_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V1u_2E0))
            & ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V5y_2E0) ) )
         => ( V4x_2E0 = V5y_2E0 ) ) ) ).

tff(thm_2Ecardinal_2EINJECTIVE__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( ( c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0) = c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V2t_2E0) )
         => ( V1s_2E0 = V2t_2E0 ) )
    <=> ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
          ( ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) )
         => ( V3x_2E0 = V4y_2E0 ) ) ) ).

tff(thm_2Ecardinal_2EFINITE__FINITE__BIGUNION,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))
     => ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0s_2E0)))
      <=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0,V0s_2E0))
           => p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2Enum__FINITE,axiom,
    ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0s_2E0))
    <=> ? [V1a_2E0: tyop_2Enum_2Enum] :
        ! [V2x_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2x_2E0,V0s_2E0))
         => p(c_2Earithmetic_2E_3C_3D_2E2(V2x_2E0,V1a_2E0)) ) ) ).

tff(thm_2Ecardinal_2Enum__FINITE__AVOID,axiom,
    ! [V0s_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,V0s_2E0))
     => ? [V1a_2E0: tyop_2Enum_2Enum] : ~ p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1a_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2Enum__INFINITE,axiom,
    ~ p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ).

tff(thm_2Ecardinal_2EHAS__SIZE__CARD,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V1n_2E0))
     => ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = V1n_2E0 ) ) ).

tff(thm_2Ecardinal_2EHAS__SIZE__0,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,c_2Enum_2E0_2E0))
    <=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).

tff(thm_2Ecardinal_2EHAS__SIZE__SUC,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,c_2Enum_2ESUC_2E1(V1n_2E0)))
    <=> ( ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) )
        & ! [V2a_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V0s_2E0))
           => p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V0s_2E0,V2a_2E0),V1n_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2EFINITE__HAS__SIZE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0) = c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2EHAS__SIZE__CLAUSES,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V1s_2E0,c_2Enum_2E0_2E0))
      <=> ( V1s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
      & ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V1s_2E0,c_2Enum_2ESUC_2E1(V0n_2E0)))
      <=> ? [V2a_2E0: A_27a,V3t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V3t_2E0,V0n_2E0))
            & ~ p(c_2Ebool_2EIN_2E2(A_27a,V2a_2E0,V3t_2E0))
            & ( V1s_2E0 = c_2Epred__set_2EINSERT_2E2(A_27a,V2a_2E0,V3t_2E0) ) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__SUBSET__EQ,axiom,
    ! [A_27a: $tType,V0a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1b_2E0))
        & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0a_2E0,V1b_2E0))
        & ( c_2Epred__set_2ECARD_2E1(A_27a,V0a_2E0) = c_2Epred__set_2ECARD_2E1(A_27a,V1b_2E0) ) )
     => ( V0a_2E0 = V1b_2E0 ) ) ).

tff(thm_2Ecardinal_2EHAS__SIZE__INDEX,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V4x_2E0: A_27a,V5m_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0,V1n_2E0),V2f_2E0),V4x_2E0),V5m_2E0))
        <=> ( p(c_2Eprim__rec_2E_3C_2E2(V5m_2E0,V1n_2E0))
            & ( app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,V5m_2E0) = V4x_2E0 ) ) )
     => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] :
          ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V1n_2E0))
         => ? [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
              ( ! [V3m_2E0: tyop_2Enum_2Enum] :
                  ( p(c_2Eprim__rec_2E_3C_2E2(V3m_2E0,V1n_2E0))
                 => p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,V3m_2E0),V0s_2E0)) )
              & ! [V4x_2E0: A_27a] :
                  ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
                 => p(c_2Ebool_2E_3F_21_2E1(tyop_2Enum_2Enum,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0,V1n_2E0),V2f_2E0),V4x_2E0))) ) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__BIGUNION__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))))] :
      ( ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1t_2E0),V0s_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0,V5x_2E0),c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0)) )
     => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
          ( ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V2m_2E0))
            & ! [V4x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
               => ( p(c_2Epred__set_2EFINITE_2E1(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0,V4x_2E0)))
                  & p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0,V4x_2E0)),V3n_2E0)) ) ) )
         => p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27b,c_2Epred__set_2EBIGUNION_2E1(A_27b,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0,V1t_2E0),V0s_2E0)))),c_2Earithmetic_2E_2A_2E2(V2m_2E0,V3n_2E0))) ) ) ).

tff(thm_2Ecardinal_2EHAS__SIZE__BOOL,axiom,
    p(c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Ebool),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) ).

tff(thm_2Ecardinal_2ECARD__BOOL,axiom,
    c_2Epred__set_2ECARD_2E1(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Ebool)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)) ).

tff(thm_2Ecardinal_2EFINITE__BOOL,axiom,
    p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Ebool,c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Ebool))) ).

tff(thm_2Ecardinal_2EHAS__SIZE__CART__UNIV,axiom,
    ! [A_27a: $tType,V0m_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),V0m_2E0))
     => p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a),c_2Earithmetic_2EEXP_2E2(V0m_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).

tff(thm_2Ecardinal_2ECARD__CART__UNIV,axiom,
    ! [A_27a: $tType] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
     => ( c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)) = c_2Earithmetic_2EEXP_2E2(c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).

tff(thm_2Ecardinal_2EFINITE__CART__UNIV,axiom,
    ! [A_27a: $tType] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)))
     => p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a))) ) ).

tff(thm_2Ecardinal_2EHAS__SIZE__NUMSEG__LT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1m_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1m_2E0,c_2Eprim__rec_2E_3C_2E2(V1m_2E0,V0n_2E0)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Enum_2Enum,c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0)),V0n_2E0)) ) ).

tff(thm_2Ecardinal_2EFINITE__NUMSEG__LT,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1m_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1m_2E0,c_2Eprim__rec_2E_3C_2E2(V1m_2E0,V0n_2E0)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0)))) ) ).

tff(thm_2Ecardinal_2EHAS__SIZE__NUMSEG__LE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1m_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1m_2E0,c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V0n_2E0)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Ecardinal_2EHAS__SIZE_2E2(tyop_2Enum_2Enum,c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0)),c_2Earithmetic_2E_2B_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ).

tff(thm_2Ecardinal_2EFINITE__NUMSEG__LE,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0),V1m_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V1m_2E0,c_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V0n_2E0)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EGSPEC_2E1(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0,V0n_2E0)))) ) ).

tff(thm_2Ecardinal_2EINFINITE__DIFF__FINITE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) )
     => ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2ELE__CASES,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0))
      | p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V0m_2E0)) ) ).

tff(thm_2Ecardinal_2ELT__CASES,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0))
      | p(c_2Eprim__rec_2E_3C_2E2(V1n_2E0,V0m_2E0))
      | ( V0m_2E0 = V1n_2E0 ) ) ).

tff(thm_2Ecardinal_2ELT,axiom,
    ( ! [V0m_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(V0m_2E0,c_2Enum_2E0_2E0) = c_2Ebool_2EF_2E0 )
    & ! [V1m_2E0: tyop_2Enum_2Enum,V2n_2E0: tyop_2Enum_2Enum] :
        ( p(c_2Eprim__rec_2E_3C_2E2(V1m_2E0,c_2Enum_2ESUC_2E1(V2n_2E0)))
      <=> ( ( V1m_2E0 = V2n_2E0 )
          | p(c_2Eprim__rec_2E_3C_2E2(V1m_2E0,V2n_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2ELT__LE,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0))
    <=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0))
        & ( V0m_2E0 != V1n_2E0 ) ) ) ).

tff(thm_2Ecardinal_2EGE,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum,V1m_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3E_3D_2E2(V1m_2E0,V0n_2E0) = c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0) ) ).

tff(thm_2Ecardinal_2ELE__SUC__LT,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(c_2Enum_2ESUC_2E1(V0m_2E0),V1n_2E0) = c_2Eprim__rec_2E_3C_2E2(V0m_2E0,V1n_2E0) ) ).

tff(thm_2Ecardinal_2EEMPTY__set__exp,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V1A_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),c_2Ecombin_2EK_2E1(tyop_2Eoption_2Eoption(A_27b),A_27a,c_2Eoption_2ENONE_2E0(A_27b)),c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))) )
      & ( ( V0B_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27c) )
       => ( c_2Ecardinal_2Eset__exp_2E2(A_27c,A_27d,c_2Epred__set_2EEMPTY_2E0(A_27d),V0B_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(A_27d))) ) ) ) ).

tff(thm_2Ecardinal_2EEMPTY__set__exp__CARD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Enum_2Enum,c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V0A_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)),c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))))) ).

tff(thm_2Ecardinal_2ESING__set__exp,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),F3_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),F1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))))] :
      ( ! [V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0: A_27b,V3b_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),F0_2E0,V1B_2E0),V0x_2E0),V3b_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2EIN_2E2(A_27a,V3b_2E0,V1B_2E0),c_2Eoption_2ESOME_2E1(A_27b,V0x_2E0),c_2Eoption_2ENONE_2E0(A_27b)) )
     => ( ! [V5b_2E0: A_27b,V0x_2E0: A_27b] :
            ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F3_2E0,V5b_2E0),V0x_2E0))
          <=> ( V5b_2E0 = V0x_2E0 ) )
       => ( ! [V0x_2E0: A_27b,V4a_2E0: A_27c,V5b_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),F2_2E0,V0x_2E0),V4a_2E0),V5b_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27c),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),F3_2E0,V5b_2E0),V0x_2E0),c_2Eoption_2ESOME_2E1(A_27c,V4a_2E0),c_2Eoption_2ENONE_2E0(A_27c)) )
         => ( ! [V0x_2E0: A_27b,V2A_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V4a_2E0: A_27c] : ( app_2E2(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))),F1_2E0,V0x_2E0),V2A_2E0),V4a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool,app_2E2(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c))),F2_2E0,V0x_2E0),V4a_2E0),c_2Ebool_2EIN_2E2(A_27c,V4a_2E0,V2A_2E0)) )
           => ! [V0x_2E0: A_27b,V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2A_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
                ( ( c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)),V1B_2E0) = c_2Epred__set_2EINSERT_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),F0_2E0,V1B_2E0),V0x_2E0),c_2Epred__set_2EEMPTY_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))) )
                & ( c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27c,V2A_2E0,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b))) = c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c,app_2E2(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Ebool))),F1_2E0,V0x_2E0),V2A_2E0)) ) ) ) ) ) ) ).

tff(thm_2Ecardinal_2ESING__set__exp__CARD,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: A_27b,V1B_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2A_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Enum_2Enum,c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)),V1B_2E0),c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))))
      & p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),A_27c,c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27c,V2A_2E0,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b))),V2A_2E0)) ) ).

tff(thm_2Ecardinal_2EPOW__TWO__set__exp,axiom,
    ! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Epred__set_2EPOW_2E1(A_27a,V0A_2E0),c_2Ecardinal_2Eset__exp_2E2(A_27a,tyop_2Enum_2Enum,c_2Epred__set_2Ecount_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V0A_2E0))) ).

tff(thm_2Ecardinal_2Eset__exp__count,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))))] :
      ( ! [V2l_2E0: tyop_2Elist_2Elist(A_27a),V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2l_2E0),V0n_2E0),V1A_2E0))
        <=> ( ( c_2Elist_2ELENGTH_2E1(A_27a,V2l_2E0) = V0n_2E0 )
            & ! [V3e_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2l_2E0)))
               => p(c_2Ebool_2EIN_2E2(A_27a,V3e_2E0,V1A_2E0)) ) ) )
     => ( ! [V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2l_2E0: tyop_2Elist_2Elist(A_27a)] : ( app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0),V1A_2E0),V2l_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,V2l_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2l_2E0),V0n_2E0),V1A_2E0)) )
       => ! [V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Elist_2Elist(A_27a),c_2Ecardinal_2Eset__exp_2E2(tyop_2Enum_2Enum,A_27a,V1A_2E0,c_2Epred__set_2Ecount_2E1(V0n_2E0)),c_2Epred__set_2EGSPEC_2E1(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool))),F0_2E0,V0n_2E0),V1A_2E0)))) ) ) ).

tff(thm_2Ecardinal_2Eset__exp__card__cong,axiom,
    ! [A_27a1: $tType,A_27a2: $tType,A_27b1: $tType,A_27b2: $tType,V0b2_2E0: tyop_2Emin_2Efun(A_27b2,tyop_2Emin_2Ebool),V1b1_2E0: tyop_2Emin_2Efun(A_27b1,tyop_2Emin_2Ebool),V2a2_2E0: tyop_2Emin_2Efun(A_27a2,tyop_2Emin_2Ebool),V3a1_2E0: tyop_2Emin_2Efun(A_27a1,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a1,A_27a2,V3a1_2E0,V2a2_2E0))
     => ( p(c_2Ecardinal_2Ecardeq_2E2(A_27b1,A_27b2,V1b1_2E0,V0b2_2E0))
       => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27b1,tyop_2Eoption_2Eoption(A_27a1)),tyop_2Emin_2Efun(A_27b2,tyop_2Eoption_2Eoption(A_27a2)),c_2Ecardinal_2Eset__exp_2E2(A_27b1,A_27a1,V3a1_2E0,V1b1_2E0),c_2Ecardinal_2Eset__exp_2E2(A_27b2,A_27a2,V2a2_2E0,V0b2_2E0))) ) ) ).

tff(thm_2Ecardinal_2Eset__exp__cardle__cong,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0d_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1c_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool),V2b_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( ( V2b_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) )
       => ( V0d_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27b) ) )
     => ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V3a_2E0,V2b_2E0))
          & p(c_2Ecardinal_2Ecardleq_2E2(A_27d,A_27b,V1c_2E0,V0d_2E0)) )
       => p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27d,tyop_2Eoption_2Eoption(A_27c)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),c_2Ecardinal_2Eset__exp_2E2(A_27d,A_27c,V3a_2E0,V1c_2E0),c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27a,V2b_2E0,V0d_2E0))) ) ) ).

tff(thm_2Ecardinal_2Eexp__INSERT__cardeq,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1e_2E0: A_27a,V2A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ebool_2EIN_2E2(A_27a,V1e_2E0,V0s_2E0))
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V2A_2E0,c_2Epred__set_2EINSERT_2E2(A_27a,V1e_2E0,V0s_2E0)),c_2Epred__set_2ECROSS_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),V2A_2E0,c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27b,V2A_2E0,V0s_2E0)))) ) ).

tff(thm_2Ecardinal_2Eexp__count__cardeq,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V1A_2E0))
        & p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0)) )
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),A_27a,c_2Ecardinal_2Eset__exp_2E2(tyop_2Enum_2Enum,A_27a,V1A_2E0,c_2Epred__set_2Ecount_2E1(V0n_2E0)),V1A_2E0)) ) ).

tff(thm_2Ecardinal_2EINFINITE__Unum,axiom,
    ! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0A_2E0))
    <=> p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0A_2E0)) ) ).

tff(thm_2Ecardinal_2Ecardleq__SURJ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1A_2E0,V0B_2E0))
    <=> ( ? [V2f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : p(c_2Epred__set_2ESURJ_2E3(A_27b,A_27a,V2f_2E0,V0B_2E0,V1A_2E0))
        | ( V1A_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ) ).

tff(thm_2Ecardinal_2EINFINITE__cardleq__INSERT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V2A_2E0))
     => ( c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,c_2Epred__set_2EINSERT_2E2(A_27b,V0x_2E0,V1s_2E0),V2A_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1s_2E0,V2A_2E0) ) ) ).

tff(thm_2Ecardinal_2Elist__EMPTY,axiom,
    ! [A_27a: $tType] : ( c_2Ecardinal_2Elist_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a)) = c_2Epred__set_2EINSERT_2E2(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0(A_27a),c_2Epred__set_2EEMPTY_2E0(tyop_2Elist_2Elist(A_27a))) ) ).

tff(thm_2Ecardinal_2Elist__SING,axiom,
    ! [A_27a: $tType,V0e_2E0: A_27a] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Ecardinal_2Elist_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0e_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a))),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ).

tff(thm_2Ecardinal_2EUNIV__list,axiom,
    ! [A_27a: $tType] : ( c_2Epred__set_2EUNIV_2E0(tyop_2Elist_2Elist(A_27a)) = c_2Ecardinal_2Elist_2E1(A_27a,c_2Epred__set_2EUNIV_2E0(A_27a)) ) ).

tff(thm_2Ecardinal_2Elist__BIGUNION__EXP,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)))] :
      ( ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1n_2E0) = c_2Ecardinal_2Eset__exp_2E2(tyop_2Enum_2Enum,A_27a,V0A_2E0,c_2Epred__set_2Ecount_2E1(V1n_2E0)) )
     => ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ecardinal_2Elist_2E1(A_27a,V0A_2E0),c_2Epred__set_2EBIGUNION_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))))) ) ).

tff(thm_2Ecardinal_2EINFINITE__A__list__BIJ__A,axiom,
    ! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0A_2E0))
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Ecardinal_2Elist_2E1(A_27a,V0A_2E0),V0A_2E0)) ) ).

tff(thm_2Ecardinal_2Efinite__subsets__bijection,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1s_2E0),V0A_2E0))
        <=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s_2E0))
            & p(c_2Epred__set_2ESUBSET_2E2(A_27a,V1s_2E0,V0A_2E0)) ) )
     => ( ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0),V1s_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1s_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0,V1s_2E0),V0A_2E0)) )
       => ! [V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0A_2E0))
           => p(c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0A_2E0,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0A_2E0)))) ) ) ) ).

tff(thm_2Ecardinal_2EFINITE__IMAGE__INJ_27,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V0s_2E0)) )
         => ( ( app_2E2(A_27a,A_27b,V1f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1f_2E0,V3y_2E0) )
          <=> ( V2x_2E0 = V3y_2E0 ) ) )
     => ( c_2Epred__set_2EFINITE_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V1f_2E0,V0s_2E0)) = c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0) ) ) ).

tff(thm_2Ecardinal_2Ecountable__decomposition,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ? [V1A_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
          ( ( c_2Epred__set_2EBIGUNION_2E1(A_27a,V1A_2E0) = V0s_2E0 )
          & ! [V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0,V1A_2E0))
             => ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V2a_2E0))
                & p(c_2Epred__set_2Ecountable_2E1(A_27a,V2a_2E0)) ) ) ) ) ).

tff(thm_2Ecardinal_2Edisjoint__countable__decomposition,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ? [V1A_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
          ( ( c_2Epred__set_2EBIGUNION_2E1(A_27a,V1A_2E0) = V0s_2E0 )
          & ! [V2a_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2a_2E0,V1A_2E0))
             => ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V2a_2E0))
                & p(c_2Epred__set_2Ecountable_2E1(A_27a,V2a_2E0)) ) )
          & ! [V3a1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4a2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
              ( ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3a1_2E0,V1A_2E0))
                & p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4a2_2E0,V1A_2E0))
                & ( V3a1_2E0 != V4a2_2E0 ) )
             => p(c_2Epred__set_2EDISJOINT_2E2(A_27a,V3a1_2E0,V4a2_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2Ecount__cardle,axiom,
    ! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2Ecount_2E1(V0n_2E0),V1A_2E0))
    <=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1A_2E0))
       => p(c_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,c_2Epred__set_2ECARD_2E1(A_27a,V1A_2E0))) ) ) ).

tff(thm_2Ecardinal_2ECANTOR,axiom,
    ! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ~ p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Epred__set_2EPOW_2E1(A_27a,V0A_2E0),V0A_2E0)) ).

tff(thm_2Ecardinal_2Ecardlt__cardle,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V0B_2E0,V1A_2E0))
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1A_2E0,V0B_2E0)) ) ).

tff(thm_2Ecardinal_2Eset__exp__product,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0B2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1B1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2A_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27c)),c_2Ecardinal_2Eset__exp_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27c)),c_2Ecardinal_2Eset__exp_2E2(A_27b,A_27c,V2A_2E0,V1B1_2E0),V0B2_2E0),c_2Ecardinal_2Eset__exp_2E2(tyop_2Epair_2Eprod(A_27b,A_27a),A_27c,V2A_2E0,c_2Epred__set_2ECROSS_2E2(A_27b,A_27a,V1B1_2E0,V0B2_2E0)))) ).

tff(thm_2Ecardinal_2ECOUNT__EQ__EMPTY,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] :
      ( ( c_2Epred__set_2Ecount_2E1(V0n_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
    <=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) ) ).

tff(thm_2Ecardinal_2EPOW__EQ__X__EXP__X,axiom,
    ! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0A_2E0))
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),c_2Epred__set_2EPOW_2E1(A_27a,V0A_2E0),c_2Ecardinal_2Eset__exp_2E2(A_27a,A_27a,V0A_2E0,V0A_2E0))) ) ).

tff(thm_2Ecardinal_2Ecardeq__bijns__cong,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0B_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1A_2E0,V0B_2E0))
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27b)),c_2Ecardinal_2Ebijns_2E1(A_27a,V1A_2E0),c_2Ecardinal_2Ebijns_2E1(A_27b,V0B_2E0))) ) ).

tff(thm_2Ecardinal_2Ebijections__cardeq,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecardinal_2Ebijns_2E1(A_27a,V0s_2E0),c_2Epred__set_2EPOW_2E1(A_27a,V0s_2E0))) ) ).

tff(thm_2Ecardinal_2ELEFT__IMP__EXISTS__THM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
      ( ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
       => p(V1Q_2E0) )
    <=> ! [V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
         => p(V1Q_2E0) ) ) ).

tff(thm_2Ecardinal_2ELEFT__IMP__FORALL__THM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Ebool] :
      ( ( ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
       => p(V1Q_2E0) )
    <=> ? [V3x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V3x_2E0))
         => p(V1Q_2E0) ) ) ).

tff(thm_2Ecardinal_2ERIGHT__IMP__EXISTS__THM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(V0P_2E0)
       => ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
    <=> ? [V3x_2E0: A_27a] :
          ( p(V0P_2E0)
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).

tff(thm_2Ecardinal_2ERIGHT__IMP__FORALL__THM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Ebool,V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(V0P_2E0)
       => ! [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V2x_2E0)) )
    <=> ! [V3x_2E0: A_27a] :
          ( p(V0P_2E0)
         => p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) ) ) ).

tff(thm_2Ecardinal_2EFINITE__FINITE__BIGUNIONS,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))
     => ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0s_2E0)))
      <=> ! [V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0,V0s_2E0))
           => p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2ECONJ__EQ__IMP,axiom,
    ! [V0r_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
      ( ( ( p(V1p_2E0)
          & p(V2q_2E0) )
       => p(V0r_2E0) )
    <=> ( p(V1p_2E0)
       => ( p(V2q_2E0)
         => p(V0r_2E0) ) ) ) ).

tff(thm_2Ecardinal_2EIMP__CONJ__ALT,axiom,
    ! [V0r_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
      ( ( ( p(V1p_2E0)
          & p(V2q_2E0) )
       => p(V0r_2E0) )
    <=> ( p(V2q_2E0)
       => ( p(V1p_2E0)
         => p(V0r_2E0) ) ) ) ).

tff(thm_2Ecardinal_2ELT__SUC__LE,axiom,
    ! [V0m_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(V0m_2E0,c_2Enum_2ESUC_2E1(V1n_2E0)) = c_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0) ) ).

tff(thm_2Ecardinal_2EINJECTIVE__ON__LEFT__INVERSE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
            & ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
         => ( V2x_2E0 = V3y_2E0 ) )
    <=> ? [V4g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
        ! [V5x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V1s_2E0))
         => ( app_2E2(A_27b,A_27a,V4g_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0)) = V5x_2E0 ) ) ) ).

tff(thm_2Ecardinal_2EINJECTIVE__LEFT__INVERSE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V1x_2E0: A_27a,V2y_2E0: A_27a] :
          ( ( app_2E2(A_27a,A_27b,V0f_2E0,V1x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V2y_2E0) )
         => ( V1x_2E0 = V2y_2E0 ) )
    <=> ? [V3g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
        ! [V4x_2E0: A_27a] : ( app_2E2(A_27b,A_27a,V3g_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0)) = V4x_2E0 ) ) ).

tff(thm_2Ecardinal_2EINTER__ACI,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,V2q_2E0,V1p_2E0) )
      & ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) )
      & ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V2q_2E0,V1p_2E0),V0r_2E0) )
      & ( c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V1p_2E0) = V1p_2E0 )
      & ( c_2Epred__set_2EINTER_2E2(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V1p_2E0),V2q_2E0) = c_2Epred__set_2EINTER_2E2(A_27a,V1p_2E0,V2q_2E0) ) ) ).

tff(thm_2Ecardinal_2ECONJ__ACI,axiom,
    ! [V0r_2E0: tyop_2Emin_2Ebool,V1p_2E0: tyop_2Emin_2Ebool,V2q_2E0: tyop_2Emin_2Ebool] :
      ( ( ( p(V1p_2E0)
          & p(V2q_2E0) )
      <=> ( p(V2q_2E0)
          & p(V1p_2E0) ) )
      & ( ( p(V1p_2E0)
          & p(V2q_2E0)
          & p(V0r_2E0) )
      <=> ( p(V1p_2E0)
          & p(V2q_2E0)
          & p(V0r_2E0) ) )
      & ( ( p(V1p_2E0)
          & p(V2q_2E0)
          & p(V0r_2E0) )
      <=> ( p(V2q_2E0)
          & p(V1p_2E0)
          & p(V0r_2E0) ) )
      & ( ( p(V1p_2E0)
          & p(V1p_2E0) )
      <=> p(V1p_2E0) )
      & ( ( p(V1p_2E0)
          & p(V1p_2E0)
          & p(V2q_2E0) )
      <=> ( p(V1p_2E0)
          & p(V2q_2E0) ) ) ) ).

tff(thm_2Ecardinal_2EUNION__ACI,axiom,
    ! [A_27a: $tType,V0r_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1p_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,V2q_2E0,V1p_2E0) )
      & ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) )
      & ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0),V0r_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V2q_2E0,V1p_2E0),V0r_2E0) )
      & ( c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V1p_2E0) = V1p_2E0 )
      & ( c_2Epred__set_2EUNION_2E2(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V1p_2E0),V2q_2E0) = c_2Epred__set_2EUNION_2E2(A_27a,V1p_2E0,V2q_2E0) ) ) ).

tff(thm_2Ecardinal_2ELT__NZ,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0))
    <=> ( V0n_2E0 != c_2Enum_2E0_2E0 ) ) ).

tff(thm_2Ecardinal_2ELE__1,axiom,
    ( ! [V0n_2E0: tyop_2Enum_2Enum] :
        ( ( V0n_2E0 != c_2Enum_2E0_2E0 )
       => p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V0n_2E0)) )
    & ! [V1n_2E0: tyop_2Enum_2Enum] :
        ( ( V1n_2E0 != c_2Enum_2E0_2E0 )
       => p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V1n_2E0)) )
    & ! [V2n_2E0: tyop_2Enum_2Enum] :
        ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V2n_2E0))
       => ( V2n_2E0 != c_2Enum_2E0_2E0 ) )
    & ! [V3n_2E0: tyop_2Enum_2Enum] :
        ( p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V3n_2E0))
       => p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V3n_2E0)) )
    & ! [V4n_2E0: tyop_2Enum_2Enum] :
        ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V4n_2E0))
       => p(c_2Eprim__rec_2E_3C_2E2(c_2Enum_2E0_2E0,V4n_2E0)) )
    & ! [V5n_2E0: tyop_2Enum_2Enum] :
        ( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),V5n_2E0))
       => ( V5n_2E0 != c_2Enum_2E0_2E0 ) ) ) ).

tff(thm_2Ecardinal_2EOR__EXISTS__THM,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( ? [V2x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V2x_2E0))
        | ? [V3x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V3x_2E0)) )
    <=> ? [V4x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0P_2E0,V4x_2E0))
          | p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1Q_2E0,V4x_2E0)) ) ) ).

tff(thm_2Ecardinal_2EBIJECTIVE__INJECTIVE__SURJECTIVE,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4y_2E0: A_27b,V5x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0f_2E0),V4y_2E0),V5x_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V1s_2E0))
            & ( app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0) = V4y_2E0 ) ) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( ( ! [V3x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
               => p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),V2t_2E0)) )
            & ! [V4y_2E0: A_27b] :
                ( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V2t_2E0))
               => p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0f_2E0),V4y_2E0))) ) )
        <=> ( ! [V6x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V1s_2E0))
               => p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V6x_2E0),V2t_2E0)) )
            & ! [V7x_2E0: A_27a,V8y_2E0: A_27a] :
                ( ( p(c_2Ebool_2EIN_2E2(A_27a,V7x_2E0,V1s_2E0))
                  & p(c_2Ebool_2EIN_2E2(A_27a,V8y_2E0,V1s_2E0))
                  & ( app_2E2(A_27a,A_27b,V0f_2E0,V7x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V8y_2E0) ) )
               => ( V7x_2E0 = V8y_2E0 ) )
            & ! [V9y_2E0: A_27b] :
                ( p(c_2Ebool_2EIN_2E2(A_27b,V9y_2E0,V2t_2E0))
               => ? [V10x_2E0: A_27a] :
                    ( p(c_2Ebool_2EIN_2E2(A_27a,V10x_2E0,V1s_2E0))
                    & ( app_2E2(A_27a,A_27b,V0f_2E0,V10x_2E0) = V9y_2E0 ) ) ) ) ) ) ).

tff(thm_2Ecardinal_2EBIJECTIVE__INVERSES,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4y_2E0: A_27b,V5x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0f_2E0),V4y_2E0),V5x_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V1s_2E0))
            & ( app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0) = V4y_2E0 ) ) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( ( ! [V3x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
               => p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0),V2t_2E0)) )
            & ! [V4y_2E0: A_27b] :
                ( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V2t_2E0))
               => p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0f_2E0),V4y_2E0))) ) )
        <=> ( ! [V6x_2E0: A_27a] :
                ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V1s_2E0))
               => p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V6x_2E0),V2t_2E0)) )
            & ? [V7g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
                ( ! [V8y_2E0: A_27b] :
                    ( p(c_2Ebool_2EIN_2E2(A_27b,V8y_2E0,V2t_2E0))
                   => p(c_2Ebool_2EIN_2E2(A_27a,app_2E2(A_27b,A_27a,V7g_2E0,V8y_2E0),V1s_2E0)) )
                & ! [V9y_2E0: A_27b] :
                    ( p(c_2Ebool_2EIN_2E2(A_27b,V9y_2E0,V2t_2E0))
                   => ( app_2E2(A_27a,A_27b,V0f_2E0,app_2E2(A_27b,A_27a,V7g_2E0,V9y_2E0)) = V9y_2E0 ) )
                & ! [V10x_2E0: A_27a] :
                    ( p(c_2Ebool_2EIN_2E2(A_27a,V10x_2E0,V1s_2E0))
                   => ( app_2E2(A_27b,A_27a,V7g_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V10x_2E0)) = V10x_2E0 ) ) ) ) ) ) ).

tff(thm_2Ecardinal_2Ele__c,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
    <=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
          ( ! [V3x_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
             => p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0),V1t_2E0)) )
          & ! [V4x_2E0: A_27a,V5y_2E0: A_27a] :
              ( ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
                & p(c_2Ebool_2EIN_2E2(A_27a,V5y_2E0,V0s_2E0))
                & ( app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V2f_2E0,V5y_2E0) ) )
             => ( V4x_2E0 = V5y_2E0 ) ) ) ) ).

tff(thm_2Ecardinal_2Elt__c,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
    <=> ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ) ).

tff(thm_2Ecardinal_2Eeq__c,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4y_2E0: A_27b,V5x_2E0: A_27a] :
          ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V2f_2E0),V4y_2E0),V5x_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0))
            & ( app_2E2(A_27a,A_27b,V2f_2E0,V5x_2E0) = V4y_2E0 ) ) )
     => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        <=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
              ( ! [V3x_2E0: A_27a] :
                  ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
                 => p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V2f_2E0,V3x_2E0),V1t_2E0)) )
              & ! [V4y_2E0: A_27b] :
                  ( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V1t_2E0))
                 => p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V2f_2E0),V4y_2E0))) ) ) ) ) ).

tff(thm_2Ecardinal_2Ege__c,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardgeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0) ) ).

tff(thm_2Ecardinal_2Egt__c,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardgt_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
    <=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ELE__C,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
    <=> ? [V2g_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] :
        ! [V3x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
         => ? [V4y_2E0: A_27b] :
              ( p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V1t_2E0))
              & ( app_2E2(A_27b,A_27a,V2g_2E0,V4y_2E0) = V3x_2E0 ) ) ) ) ).

tff(thm_2Ecardinal_2EGE__C,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardgeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
    <=> ? [V2f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
        ! [V3y_2E0: A_27b] :
          ( p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1t_2E0))
         => ? [V4x_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V0s_2E0))
              & ( V3y_2E0 = app_2E2(A_27a,A_27b,V2f_2E0,V4x_2E0) ) ) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE,axiom,
    ! [A_27a: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27a,V0t_2E0) = c_2Ecardinal_2Ecardgeq_2E2(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0t_2E0) ) ).

tff(thm_2Ecardinal_2EEQ__C,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V5x_2E0: A_27a,V6y_2E0: A_27b] :
          ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V1t_2E0),V2R_2E0),V5x_2E0),V6y_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27b,V6y_2E0,V1t_2E0))
            & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V2R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V5x_2E0,V6y_2E0))) ) )
     => ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V7y_2E0: A_27b,V8x_2E0: A_27a] :
            ( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0s_2E0),V2R_2E0),V7y_2E0),V8x_2E0))
          <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V8x_2E0,V0s_2E0))
              & p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V2R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V8x_2E0,V7y_2E0))) ) )
       => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
            ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
          <=> ? [V2R_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)] :
                ( ! [V3x_2E0: A_27a,V4y_2E0: A_27b] :
                    ( p(app_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,V2R_2E0,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V4y_2E0)))
                   => ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V0s_2E0))
                      & p(c_2Ebool_2EIN_2E2(A_27b,V4y_2E0,V1t_2E0)) ) )
                & ! [V5x_2E0: A_27a] :
                    ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V0s_2E0))
                   => p(c_2Ebool_2E_3F_21_2E1(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V1t_2E0),V2R_2E0),V5x_2E0))) )
                & ! [V7y_2E0: A_27b] :
                    ( p(c_2Ebool_2EIN_2E2(A_27b,V7y_2E0,V1t_2E0))
                   => p(c_2Ebool_2E_3F_21_2E1(A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F1_2E0,V0s_2E0),V2R_2E0),V7y_2E0))) ) ) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__LE__REFL,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).

tff(thm_2Ecardinal_2ECARD__LE__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LT__REFL,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ~ ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).

tff(thm_2Ecardinal_2ECARD__LET__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V2u_2E0,V1t_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LTE__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LT__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V2u_2E0,V1t_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__REFL,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0)) ).

tff(thm_2Ecardinal_2ECARD__EQ__SYM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__IMP__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LT__IMP__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LE__RELATIONAL,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))))] :
      ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5y_2E0: A_27b] :
          ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V1s_2E0),V0R_2E0),V5y_2E0))
        <=> ? [V6x_2E0: A_27a] :
              ( p(c_2Ebool_2EIN_2E2(A_27a,V6x_2E0,V1s_2E0))
              & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V6x_2E0),V5y_2E0)) ) )
     => ( ! [V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V5y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0R_2E0),V5y_2E0) = c_2Epair_2E_2C_2E2(A_27b,tyop_2Emin_2Ebool,V5y_2E0,app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),F1_2E0,V1s_2E0),V0R_2E0),V5y_2E0)) )
       => ! [V0R_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ! [V2x_2E0: A_27a,V3y_2E0: A_27b,V4y_27_2E0: A_27b] :
                ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
                  & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V3y_2E0))
                  & p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0R_2E0,V2x_2E0),V4y_27_2E0)) )
               => ( V3y_2E0 = V4y_27_2E0 ) )
           => p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,c_2Epred__set_2EGSPEC_2E1(A_27b,A_27b,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),F0_2E0,V1s_2E0),V0R_2E0)),V1s_2E0)) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__LE__EMPTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
    <=> ( V0x_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__EMPTY,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,c_2Epred__set_2EEMPTY_2E0(A_27b)))
    <=> ( V0s_2E0 = c_2Epred__set_2EEMPTY_2E0(A_27a) ) ) ).

tff(thm_2Ecardinal_2ECARD__LE__ANTISYM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) )
    <=> p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LE__TOTAL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
      | p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LET__TOTAL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
      | ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LTE__TOTAL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
      | p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LT__TOTAL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
      | ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
      | ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__NOT__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
    <=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__NOT__LT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ~ ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
    <=> p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LT__LE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
    <=> ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & ~ p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARD__LE__LT,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0))
    <=> ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1s2_2E0,V0s1_2E0))
        | p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s1_2E0,V1s2_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARD__LE__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1s_27_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,V2t_2E0,V3t_27_2E0)) )
     => ( c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27c,V0s_2E0,V2t_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27d,V1s_27_2E0,V3t_27_2E0) ) ) ).

tff(thm_2Ecardinal_2ECARD__LT__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1s_27_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,V2t_2E0,V3t_27_2E0)) )
     => ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2t_2E0,V0s_2E0))
      <=> ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27d,A_27b,V3t_27_2E0,V1s_27_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__TRANS,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)) )
     => p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1s_27_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,V2t_2E0,V3t_27_2E0)) )
     => ( c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27c,V0s_2E0,V2t_2E0) = c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27d,V1s_27_2E0,V3t_27_2E0) ) ) ).

tff(thm_2Ecardinal_2EINFINITE__CARD__LE,axiom,
    ! [A_27a: $tType,V0A_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0A_2E0))
    <=> p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0A_2E0)) ) ).

tff(thm_2Ecardinal_2EFINITE__CARD__LT,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
    <=> ~ p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Enum_2Enum,A_27a,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LE__SUBSET,axiom,
    ! [A_27a: $tType,V0x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1y_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0x_2E0,V1y_2E0))
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0x_2E0,V1y_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LE__UNIV,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,c_2Epred__set_2EUNIV_2E0(A_27a))) ).

tff(thm_2Ecardinal_2ECARD__LE__EQ__SUBSET,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
    <=> ? [V2u_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(c_2Epred__set_2ESUBSET_2E2(A_27b,V2u_2E0,V1t_2E0))
          & p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V2u_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARD__INFINITE__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
     => ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
      <=> ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARD__FINITE__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
     => ( c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0) = c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0) ) ) ).

tff(thm_2Ecardinal_2ECARD__LE__FINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__FINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1t_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,V0s_2E0,V1t_2E0)) )
     => p(c_2Epred__set_2EFINITE_2E1(A_27b,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LE__INFINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LT__FINITE__INFINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & ~ p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LE__CARD__IMP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => p(c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__CARD__IMP,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0) ) ) ).

tff(thm_2Ecardinal_2ECARD__LE__CARD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) )
     => ( c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__CARD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) )
     => ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))
      <=> ( c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__ADD__C,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) )
     => ( c_2Epred__set_2ECARD_2E1(tyop_2Esum_2Esum(A_27a,A_27b),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARD__ADD__SYM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(A_27a,A_27b),tyop_2Esum_2Esum(A_27b,A_27a),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),c_2Ecardinal_2E_2B__c_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))) ).

tff(thm_2Ecardinal_2ECARD__ADD__ASSOC,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Esum_2Esum(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),c_2Ecardinal_2E_2B__c_2E2(A_27a,tyop_2Esum_2Esum(A_27b,A_27c),V0s_2E0,c_2Ecardinal_2E_2B__c_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)),c_2Ecardinal_2E_2B__c_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27c,c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),V2u_2E0))) ).

tff(thm_2Ecardinal_2ECARD__MUL__SYM,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27b,A_27a),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))) ).

tff(thm_2Ecardinal_2ECARD__MUL__ASSOC,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c),c_2Epred__set_2ECROSS_2E2(A_27a,tyop_2Epair_2Eprod(A_27b,A_27c),V0s_2E0,c_2Epred__set_2ECROSS_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)),c_2Epred__set_2ECROSS_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c,c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),V2u_2E0))) ).

tff(thm_2Ecardinal_2ECARD__LDISTRIB,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,tyop_2Esum_2Esum(A_27b,A_27c)),tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c)),c_2Epred__set_2ECROSS_2E2(A_27a,tyop_2Esum_2Esum(A_27b,A_27c),V0s_2E0,c_2Ecardinal_2E_2B__c_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)),c_2Ecardinal_2E_2B__c_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27c),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0)))) ).

tff(thm_2Ecardinal_2ECARD__RDISTRIB,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(tyop_2Esum_2Esum(A_27a,A_27b),A_27c),tyop_2Esum_2Esum(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c)),c_2Epred__set_2ECROSS_2E2(tyop_2Esum_2Esum(A_27a,A_27b),A_27c,c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0),V2u_2E0),c_2Ecardinal_2E_2B__c_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27c),c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,V0s_2E0,V2u_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27c,V1t_2E0,V2u_2E0)))) ).

tff(thm_2Ecardinal_2ECARD__LE__ADDR,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27b),V0s_2E0,c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))) ).

tff(thm_2Ecardinal_2ECARD__LE__ADDL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27b,tyop_2Esum_2Esum(A_27a,A_27b),V1t_2E0,c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))) ).

tff(thm_2Ecardinal_2ECARD__ADD__LE__MUL__INFINITE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27a,A_27a),tyop_2Epair_2Eprod(A_27a,A_27a),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0),c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__MUL__FINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0P_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1Q_2E0)) )
     => p(c_2Epred__set_2EFINITE_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0P_2E0,V1Q_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__ADD__FINITE__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(tyop_2Esum_2Esum(A_27a,A_27b),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)))
    <=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARD__ADD__FINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) )
     => p(c_2Epred__set_2EFINITE_2E1(tyop_2Esum_2Esum(A_27a,A_27b),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__SQUARE__INFINITE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27a),A_27a,c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0),V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__DISJOINT__UNION,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0) = c_2Epred__set_2EEMPTY_2E0(A_27a) )
     => p(c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27a),c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27a,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2EUNION__LE__ADD__C,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Esum_2Esum(A_27a,A_27a),c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27a,V0s_2E0,V1t_2E0))) ).

tff(thm_2Ecardinal_2ECARD__SQUARE__NUM,axiom,
    p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum,c_2Epred__set_2ECROSS_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ).

tff(thm_2Ecardinal_2ECARD__LE__SQUARE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a),V0s_2E0,c_2Epred__set_2ECROSS_2E2(A_27a,A_27a,V0s_2E0,V0s_2E0))) ).

tff(thm_2Ecardinal_2EIN__CARD__MUL,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] :
      ( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)))
    <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
        & p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1t_2E0)) ) ) ).

tff(thm_2Ecardinal_2EIN__CARD__ADD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINL_2E1(A_27a,A_27b,V2x_2E0),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0)) = c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0) )
      & ! [V3y_2E0: A_27b] : ( c_2Ebool_2EIN_2E2(tyop_2Esum_2Esum(A_27a,A_27b),c_2Esum_2EINR_2E1(A_27a,A_27b,V3y_2E0),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27b,V1s_2E0,V0t_2E0)) = c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V0t_2E0) ) ) ).

tff(thm_2Ecardinal_2ECARD__MUL__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1s_27_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,V2t_2E0,V3t_27_2E0)) )
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,V0s_2E0,V2t_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27d,V1s_27_2E0,V3t_27_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__ADD__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1s_27_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27c,A_27d,V2t_2E0,V3t_27_2E0)) )
     => p(c_2Ecardinal_2Ecardeq_2E2(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27c,V0s_2E0,V2t_2E0),c_2Ecardinal_2E_2B__c_2E2(A_27b,A_27d,V1s_27_2E0,V3t_27_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__LE__MUL,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1s_27_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27d,V2t_2E0,V3t_27_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Epair_2Eprod(A_27b,A_27d),c_2Epred__set_2ECROSS_2E2(A_27a,A_27c,V0s_2E0,V2t_2E0),c_2Epred__set_2ECROSS_2E2(A_27b,A_27d,V1s_27_2E0,V3t_27_2E0))) ) ).

tff(thm_2Ecardinal_2ECARD__LE__ADD,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_27_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),V3t_27_2E0: tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V0s_2E0,V1s_27_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27d,V2t_2E0,V3t_27_2E0)) )
     => p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Esum_2Esum(A_27a,A_27c),tyop_2Esum_2Esum(A_27b,A_27d),c_2Ecardinal_2E_2B__c_2E2(A_27a,A_27c,V0s_2E0,V2t_2E0),c_2Ecardinal_2E_2B__c_2E2(A_27b,A_27d,V1s_27_2E0,V3t_27_2E0))) ) ).

tff(thm_2Ecardinal_2Emul__c,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))))] :
      ( ! [V2x_2E0: A_27a,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3y_2E0: A_27b,V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0s_2E0),V3y_2E0),V1t_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27b,V3y_2E0,V1t_2E0)) ) )
     => ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2x_2E0: A_27a,V3y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0s_2E0),V1t_2E0),V2x_2E0),V3y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27b,V2x_2E0,V3y_2E0),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V2x_2E0),V0s_2E0),V3y_2E0),V1t_2E0)) )
       => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0) = c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)))),F0_2E0,V0s_2E0),V1t_2E0))) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
            & ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
         => ( V2x_2E0 = V3y_2E0 ) )
     => p(c_2Ecardinal_2Ecardeq_2E2(A_27b,A_27a,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),V1s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LE__IMAGE__GEN,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(A_27b,V2t_2E0,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)))
     => p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V2t_2E0,V1s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LE__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0),V1s_2E0)) ).

tff(thm_2Ecardinal_2ECARD__HAS__SIZE__CONG,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2n_2E0: tyop_2Enum_2Enum] :
      ( ( p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27a,V0s_2E0,V2n_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0)) )
     => p(c_2Ecardinal_2EHAS__SIZE_2E2(A_27b,V1t_2E0,V2n_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__LT__CARD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V1t_2E0)) )
     => ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27b,A_27a,V1t_2E0,V0s_2E0))
      <=> p(c_2Eprim__rec_2E_3C_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V0s_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V1t_2E0))) ) ) ).

tff(thm_2Ecardinal_2ECARDLEQ__CARD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V0s2_2E0)) )
     => ( c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0) = c_2Earithmetic_2E_3C_3D_2E2(c_2Epred__set_2ECARD_2E1(A_27a,V1s1_2E0),c_2Epred__set_2ECARD_2E1(A_27b,V0s2_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECARDEQ__CARD__EQN,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V0s2_2E0)) )
     => ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0))
      <=> ( c_2Epred__set_2ECARD_2E1(A_27a,V1s1_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V0s2_2E0) ) ) ) ).

tff(thm_2Ecardinal_2ECARD__CARDEQ__I,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1s1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V1s1_2E0))
        & p(c_2Epred__set_2EFINITE_2E1(A_27b,V0s2_2E0))
        & ( c_2Epred__set_2ECARD_2E1(A_27a,V1s1_2E0) = c_2Epred__set_2ECARD_2E1(A_27b,V0s2_2E0) ) )
     => p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27b,V1s1_2E0,V0s2_2E0)) ) ).

tff(thm_2Ecardinal_2EBIJ__functions__agree,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V0f_2E0,V2s_2E0,V3t_2E0))
        & ! [V4x_2E0: A_27a] :
            ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V2s_2E0))
           => ( app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V4x_2E0) ) ) )
     => p(c_2Epred__set_2EBIJ_2E3(A_27a,A_27b,V1g_2E0,V2s_2E0,V3t_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__MUL__LT__INFINITE,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2u_2E0: tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)] :
      ( ( ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27a,V2u_2E0,V0s_2E0))
        & ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,A_27b,V2u_2E0,V1t_2E0))
        & ~ p(c_2Epred__set_2EFINITE_2E1(A_27c,V2u_2E0)) )
     => ~ p(c_2Ecardinal_2Ecardleq_2E2(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b),V2u_2E0,c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2ECANTOR__THM,axiom,
    ! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))] :
      ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0s_2E0),V1t_2E0) = c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1t_2E0,c_2Epred__set_2ESUBSET_2E2(A_27a,V1t_2E0,V0s_2E0)) )
     => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ~ p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Epred__set_2EGSPEC_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0,V0s_2E0)),V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECANTOR__THM__UNIV,axiom,
    ! [A_27a: $tType] : ~ p(c_2Ecardinal_2Ecardleq_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a,c_2Epred__set_2EUNIV_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNIV_2E0(A_27a))) ).

tff(thm_2Ecardinal_2ENUM__COUNTABLE,axiom,
    p(c_2Epred__set_2Ecountable_2E1(tyop_2Enum_2Enum,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ).

tff(thm_2Ecardinal_2ECOUNTABLE__ALT__cardleq,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0) = c_2Ecardinal_2Ecardleq_2E2(A_27a,tyop_2Enum_2Enum,V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__CASES,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
    <=> ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
        | p(c_2Ecardinal_2Ecardeq_2E2(A_27a,tyop_2Enum_2Enum,V0s_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum))) ) ) ).

tff(thm_2Ecardinal_2ECARD__LE__COUNTABLE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0))
        & p(c_2Ecardinal_2Ecardleq_2E2(A_27a,A_27a,V0s_2E0,V1t_2E0)) )
     => p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__EQ__COUNTABLE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0))
        & p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,V0s_2E0,V1t_2E0)) )
     => p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECARD__COUNTABLE__CONG,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ecardinal_2Ecardeq_2E2(A_27a,A_27a,V0s_2E0,V1t_2E0))
     => ( c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0) = c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__RESTRICT,axiom,
    ! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V2x_2E0: A_27a,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2x_2E0),V0s_2E0),V1P_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V0s_2E0))
            & p(app_2E2(A_27a,tyop_2Emin_2Ebool,V1P_2E0,V2x_2E0)) ) )
     => ( ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V1P_2E0),V2x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V2x_2E0,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F1_2E0,V2x_2E0),V0s_2E0),V1P_2E0)) )
       => ! [V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
           => p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0s_2E0),V1P_2E0)))) ) ) ) ).

tff(thm_2Ecardinal_2EFINITE__IMP__COUNTABLE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0)) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__IMAGE,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0))
     => p(c_2Epred__set_2Ecountable_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0))) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__IMAGE__INJ__GENERAL,axiom,
    ! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))))] :
      ( ! [V5x_2E0: A_27a,V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V5x_2E0),V2s_2E0),V0f_2E0),V1A_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,V2s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V5x_2E0),V1A_2E0)) ) )
     => ( ! [V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V5x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2s_2E0),V0f_2E0),V1A_2E0),V5x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V5x_2E0,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),F1_2E0,V5x_2E0),V2s_2E0),V0f_2E0),V1A_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( ( ! [V3x_2E0: A_27a,V4y_2E0: A_27a] :
                  ( ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V2s_2E0))
                    & p(c_2Ebool_2EIN_2E2(A_27a,V4y_2E0,V2s_2E0))
                    & ( app_2E2(A_27a,A_27b,V0f_2E0,V3x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V4y_2E0) ) )
                 => ( V3x_2E0 = V4y_2E0 ) )
              & p(c_2Epred__set_2Ecountable_2E1(A_27b,V1A_2E0)) )
           => p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0,V2s_2E0),V0f_2E0),V1A_2E0)))) ) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__IMAGE__INJ__EQ,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
          ( ( p(c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,V1s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27a,V3y_2E0,V1s_2E0))
            & ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) ) )
         => ( V2x_2E0 = V3y_2E0 ) )
     => ( c_2Epred__set_2Ecountable_2E1(A_27b,c_2Epred__set_2EIMAGE_2E2(A_27a,A_27b,V0f_2E0,V1s_2E0)) = c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__IMAGE__INJ,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))))] :
      ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1A_2E0),V4x_2E0) = c_2Epair_2E_2C_2E2(A_27a,tyop_2Emin_2Ebool,V4x_2E0,c_2Ebool_2EIN_2E2(A_27b,app_2E2(A_27a,A_27b,V0f_2E0,V4x_2E0),V1A_2E0)) )
     => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1A_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
          ( ( ! [V2x_2E0: A_27a,V3y_2E0: A_27a] :
                ( ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V0f_2E0,V3y_2E0) )
               => ( V2x_2E0 = V3y_2E0 ) )
            & p(c_2Epred__set_2Ecountable_2E1(A_27b,V1A_2E0)) )
         => p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EGSPEC_2E1(A_27a,A_27a,app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0,V0f_2E0),V1A_2E0)))) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__EMPTY,axiom,
    ! [A_27a: $tType] : p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EEMPTY_2E0(A_27a))) ).

tff(thm_2Ecardinal_2ECOUNTABLE__INTER,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
        | p(c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0)) )
     => p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EINTER_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__UNION__IMP,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0)) )
     => p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__UNION,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EUNION_2E2(A_27a,V0s_2E0,V1t_2E0)))
    <=> ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0)) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__SING,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))) ).

tff(thm_2Ecardinal_2ECOUNTABLE__INSERT,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EINSERT_2E2(A_27a,V0x_2E0,V1s_2E0)) = c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__DELETE,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EDELETE_2E2(A_27a,V1s_2E0,V0x_2E0)) = c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__DIFF__FINITE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0))
     => ( c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,V1t_2E0,V0s_2E0)) = c_2Epred__set_2Ecountable_2E1(A_27a,V1t_2E0) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__CROSS,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1t_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
        & p(c_2Epred__set_2Ecountable_2E1(A_27b,V1t_2E0)) )
     => p(c_2Epred__set_2Ecountable_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epred__set_2ECROSS_2E2(A_27a,A_27b,V0s_2E0,V1t_2E0))) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__AS__IMAGE__SUBSET,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
     => ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__AS__IMAGE__SUBSET__EQ,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
    <=> ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : p(c_2Epred__set_2ESUBSET_2E2(A_27a,V0s_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__AS__IMAGE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
        & ( V0s_2E0 != c_2Epred__set_2EEMPTY_2E0(A_27a) ) )
     => ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : ( V0s_2E0 = c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)) ) ) ).

tff(thm_2Ecardinal_2EFORALL__COUNTABLE__AS__IMAGE,axiom,
    ! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ! [V1d_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
          ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V1d_2E0))
         => p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1d_2E0)) )
    <=> ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EEMPTY_2E0(A_27a)))
        & ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] : p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,V2f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)))) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__AS__INJECTIVE__IMAGE,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V0s_2E0))
        & ~ p(c_2Epred__set_2EFINITE_2E1(A_27a,V0s_2E0)) )
     => ? [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)] :
          ( ( V0s_2E0 = c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,c_2Epred__set_2EUNIV_2E0(tyop_2Enum_2Enum)) )
          & ! [V2m_2E0: tyop_2Enum_2Enum,V3n_2E0: tyop_2Enum_2Enum] :
              ( ( app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V2m_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,V1f_2E0,V3n_2E0) )
             => ( V2m_2E0 = V3n_2E0 ) ) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__BIGUNION,axiom,
    ! [A_27a: $tType,V0s_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2Ecountable_2E1(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))
        & ! [V1x_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
            ( p(c_2Ebool_2EIN_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_2E0,V0s_2E0))
           => p(c_2Epred__set_2Ecountable_2E1(A_27a,V1x_2E0)) ) )
     => p(c_2Epred__set_2Ecountable_2E1(A_27a,c_2Epred__set_2EBIGUNION_2E1(A_27a,V0s_2E0))) ) ).

tff(thm_2Ecardinal_2EIN__ELIM__PAIR__THM,axiom,
    ! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))))] :
      ( ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3x_2E0: A_27a,V4y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0),V3x_2E0),V4y_2E0) = c_2Epair_2E_2C_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool,c_2Epair_2E_2C_2E2(A_27a,A_27b,V3x_2E0,V4y_2E0),app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V3x_2E0),V4y_2E0)) )
     => ! [V0P_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1a_2E0: A_27a,V2b_2E0: A_27b] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(A_27a,A_27b,V1a_2E0,V2b_2E0),c_2Epred__set_2EGSPEC_2E1(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool))),F0_2E0,V0P_2E0)))) = app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0P_2E0,V1a_2E0),V2b_2E0) ) ) ).

tff(thm_2Ecardinal_2ECOUNTABLE__PRODUCT__DEPENDENT,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))))] :
      ( ! [V4x_2E0: A_27a,V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V5y_2E0: A_27b,V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
          ( p(app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),F1_2E0,V4x_2E0),V1s_2E0),V5y_2E0),V2t_2E0))
        <=> ( p(c_2Ebool_2EIN_2E2(A_27a,V4x_2E0,V1s_2E0))
            & p(c_2Ebool_2EIN_2E2(A_27b,V5y_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0,V4x_2E0))) ) )
     => ( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4x_2E0: A_27a,V5y_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))),F0_2E0,V0f_2E0),V1s_2E0),V2t_2E0),V4x_2E0),V5y_2E0) = c_2Epair_2E_2C_2E2(A_27c,tyop_2Emin_2Ebool,app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V4x_2E0),V5y_2E0),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool))),F1_2E0,V4x_2E0),V1s_2E0),V5y_2E0),V2t_2E0)) )
       => ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1s_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2t_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))] :
            ( ( p(c_2Epred__set_2Ecountable_2E1(A_27a,V1s_2E0))
              & ! [V3x_2E0: A_27a] :
                  ( p(c_2Ebool_2EIN_2E2(A_27a,V3x_2E0,V1s_2E0))
                 => p(c_2Epred__set_2Ecountable_2E1(A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2t_2E0,V3x_2E0))) ) )
           => p(c_2Epred__set_2Ecountable_2E1(A_27c,c_2Epred__set_2EGSPEC_2E1(A_27c,tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2EUNCURRY_2E1(A_27a,A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))))),F0_2E0,V0f_2E0),V1s_2E0),V2t_2E0))))) ) ) ) ).

%------------------------------------------------------------------------------